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Theorem con34b 283
Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
con34b  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )

Proof of Theorem con34b
StepHypRef Expression
1 con3 126 . 2  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
2 ax-3 7 . 2  |-  ( ( -.  ps  ->  -.  ph )  ->  ( ph  ->  ps ) )
31, 2impbii 180 1  |-  ( (
ph  ->  ps )  <->  ( -.  ps  ->  -.  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  mtt  329  pm4.14  561  dfom2  4658  weniso  5852  dfsup2  7195  wemapso2lem  7265  pwfseqlem3  8282  indstr  10287  rpnnen2  12504  algcvgblem  12747  isirred2  15483  isdomn2  16040  ist0-3  17073  mdegleb  19450  dchrelbas4  20482  ltl4ev  24992  supnuf  25629  supexr  25631  raldifsni  26753  isdomn3  27523  conss34  27645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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